where \(\alpha =e^2/4\pi \) , \(C_0^A = C_0(0,M_A^2,s; M_f,M_f,M_f)\)  is the Passarino-Veltman loop function as defined in Ref. [1]} and \(n_\chi \)  is the dark matter charge under \(\,{\rm U}(1)_B\) . In order to predict the cross-sections for these quantum mechanical processes we need to use the interactions
of the new fields required for anomaly cancellation.
